# BD bisects <ABC. Solve for x and find m<ABC. m<ABD=7x-5, m<CBD=4x+1 x=?

Question
BD bisects $$\displaystyle{<}{A}{B}{C}$$</span>. Solve for x and find m$$\displaystyle{m}{<}{A}{B}{D}={7}{x}-{5},{m}{<}{C}{B}{D}={4}{x}+{1}$$</span> x=?

2021-02-12
Given:
$$\displaystyle{m}∠{A}{B}{D}={7}{x}−{5}$$
m∠CBD=4x+1ZSK
BD bisects $$\displaystyle∠{A}{B}{C}$$
x=?
When BD bisects $$\displaystyle∠{A}{B}{C}$$ then $$\displaystyle∠{A}{B}{D}=∠{D}{B}{C}$$
7x−5=4x+1
Subtract 4x both the sides:
7x−5−4x=4x+1
3x−5=1
3x−5+5=1+5
3x=6
Divide 3 by both the sides:
3x3=63
x=2
Hence value of x ix 2

### Relevant Questions

Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground and his line of sight to the observation deck as $$\displaystyle{77}^{\circ}$$. How far is Aidan from the base of the Lookout to the nearest metre?

In any triangle ABC, E and D are interior points of AC and BC,respectively. AF bisects angle CAD and BF bisects angle CBE. Prove that measures (AEB) + measure (ADB) = 2x measure of (AFB).
In triangle ABC, a=5, $$\displaystyle{M}{<}{B}={92}°$$, c=3. Find b.
Find all rational zeros of the polynomial, and write the polynomial in factored form.
$$\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}+{7}{x}^{{{2}}}+{4}{x}-{4}$$
Find all rational zeros of the polynomial, and write the polynomial in factored form.
$$\displaystyle{P}{\left({x}\right)}={4}{x}^{{{3}}}-{7}{x}+{3}$$
Higher-order derivatives Find ƒ'(x), ƒ''(x), and ƒ'''(x) for the following functions.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}-{7}{x}-{8}}}{{{x}+{1}}}}$$
One side of an equilateral triangle is given. Solve for the other sides.
3 ft
1 in.
93 m
8.4 yd
$$\displaystyle{8}\frac{{3}}{{4}}{c}{m}$$
The following are the dimensions of a few rectangles. Find the are of the two right triangles that are cut from the rectangles using the formmula of the area of a triangle.
A. Lenght= 13.5 m, Breadth=10.5 m
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors $$\displaystyle\hat{{{i}}}$$ and $$\displaystyle\hat{{{j}}}$$.
1. (Enter in box 1) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+$$
5. ( Enter in box 5) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$